Profit (or) gain = Selling price - Cost price
Loss = Cost price - Selling price
Profit % = (Profit / Cost price) ⋅ 100
Loss % = (Loss / Cost price) ⋅ 100
Cost price = [100 / (100 - loss%)] ⋅ Selling price
Cost price = [100 / (100 + profit%)] ⋅ Selling price
Selling price = [(100 + profit%)/100] ⋅ Cost price
Selling price = [(100 - loss%)/100] ⋅ Cost price
Example 1 :
A shop purchased some tennis rackets at $150 each. It then sold them at $175 each. When the shop was left with 8 rackets, the proceeds had covered the initial total cost price plus profit of $525. How many tennis rackets did the shop purchased at first ?
Solution :
By selling 8 rackets the shops earns with profit
= 8(175) + 525
= 1400 + 525
= 1925
Cost price of 1 racket = 150
Selling price of 1 racket = 175
Profit = 175 - 150
= 25
Number of rackets = Total profit earned / profit earned in one
= 1925/25
Number of rackets earned = 77
Example 2 :
When a plot is sold for $18700, the owner loses 15%. At what price must the plot be sold in order to gain 15% ?
Solution :
Selling price of the plot = $18700
Let x be the cost price
x - 15% of x = 18700
85% of x = 18700
x = 18700/0.85
x = 22000
To get the profit of 15% profit, we should find 115% of cost price.
= 115% of 22000
= 1.15(22000)
= 25300
Hence the required selling price is 25300.
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